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Galois Groups and Fundamental Groups
Ever since the concepts of Galois groups in algebra and fundamental groups in topology emerged during the nineteenth century, mathematicians have known of the strong analogies between the two concepts. This book presents the connection starting at an elementary level, showing how the judicious use of algebraic geometry gives access to the powerful interplay between algebra and topology that underpins much modern research in geometry and number theory. Assuming as little technical background as possible, the book starts with basic algebraic and topological concepts, but already presented from the modern viewpoint advocated by Grothendieck. This enables a systematic yet accessible development of the theories of fundamental groups of algebraic curves, fundamental groups of schemes, and Tannakian fundamental groups. The connection between fundamental groups and linear differential equations is also developed at increasing levels of generality. Key applications and recent results, for example on the inverse Galois problem, are given throughout.
OT Report
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Tracking Control of Networked Systems via Sliding-Mode
The book focuses on the research methods of networked control systems via sliding mode. The problems with network disturbances, network induced delay, out-of-sequence and packet loss, and network attacks are studied in detail. The content studied in this book is introduced in detail and is verified by simulation or experiment. It is especially suitable for readers who are interested in learning the control scheme of networked systems. This book can benefit researchers, engineers, and students in related fields such as electrical, control, automation, and cyber security.
Education Directory
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Modelling and Planning for Sensor Based Intelligent Robot Systems
This edited and reviewed volume consists of papers that were originally presented at a workshop in the Scientific Center at Schloss Dagstuhl, Germany. It gives an overview of the field and presents the latest developments in the areas of modeling and planning for sensor based robots. The particular topics addressed include active vision, sensor fusion, environment modeling, motion planning, robot navigation, distributed control architectures, reactive behavior, and others.
